High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients |
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| Authors: | Chao Yue |
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| Institution: | 1. School of Economics and Trade, Zhengzhou University of Aeronautics, Zhengzhou, China;2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China |
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| Abstract: | In this paper, we first propose the so‐called improved split‐step theta methods for non‐autonomous stochastic differential equations driven by non‐commutative noise. Then, we prove that the improved split‐step theta method is convergent with strong order of one for stochastic differential equations with the drift coefficient satisfying a superlinearly growing condition and a one‐sided Lipschitz continuous condition. Finally, the obtained results are verified by numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | stochastic differential equations one‐sided Lipschitz condition improved split‐step theta methods strong convergence superlinearly growing condition |
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